Problem: $A$ $B$ $C$ If: $ AC = 69$, $ BC = 3x + 2$, and $ AB = 6x + 4$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 4} + {3x + 2} = {69}$ Combine like terms: $ 9x + 6 = {69}$ Subtract $6$ from both sides: $ 9x = 63$ Divide both sides by $9$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 3({7}) + 2$ Simplify: $ {BC = 21 + 2}$ Simplify to find ${BC}$ : $ {BC = 23}$